The cahn-hilliard equation with dynamic boundary conditions

Abstract

This paper is concerned with the following Cahn-Hilliard equation ψt = δμ, where μ =-δψ-ψ + ψ3, subject on the boundary τ to the following dynamic boundary condition σsδ||ψ-∂vψ+hs-gsψ = 1/τsψt and ∂μ = 0, and the initial condition ψ|t=0 = ψ0. This problem was recently proposed by physicists to describe spinodal decomposition of binary mixtures where the effective interaction between the wall (i.e., the boundary γ) and two mixture components are short-ranged. The global existence and uniqueness of solutions to this initial boundary value problem with highest-order boundary conditions is proved.